The Butcher--Oemler effect at z~0.35: a change in perspective

0.51 MB·English

by  S. Andreon

Mon.Not.R.Astron.Soc.000,1–16(2004) Printed5February2008 (MNLATEXstylefilev2.2)
z ∼ 0.35
The Butcher–Oemler effect at : a change in
perspective.
S. Andreon,1⋆ H. Quintana,2 M. Tajer,1 G. Galaz,2 J. Surdej,3
1INAF–Osservatorio Astronomico di Brera, Milano, Italy
2Departamento de Astronom´ıa y Astrof´ısica, Pontificia Universidad Cat´olica de Chile, Santiago, Chile
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3Institut d’Astrophysique et de G´eophysique, Universit´ede Li`ege, Sart Tilman, Belgium
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Accepted ...Received...
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ABSTRACT

1
v The present paper focuses on the much debated Butcher-Oemler effect: the in-
7 crease with redshift of the fraction of blue galaxies in clusters. Considering a repre-
6 sentative cluster sample made of seven group/clusters at z ∼0.35, we have measured
1 the blue fraction from the cluster core to the cluster outskirts and the field mainly
1 using wide fieldCTIO images.This samplerepresentsa randomselectionofa volume
0 completex-rayselectedclustersample,selectedsothatthereisnophysicalconnection
6 with the studied quantity (blue fraction), to minimize observational biases. In order
0
to statistically assess the significance of the Butcher–Oemler effect, we introduce the
/
h tools of Bayesian inference. Furthermore, we modified the blue fraction definition in
p orderto takeintoaccountthe reducedageofthe universeathigherredshifts,because
- we should no longer attempt to reject an unphysical universe in which the age of the
o
Universe does depend on redshift, whereas the age of its content does not. We mea-
r
t suredthe bluefractionfromtheclustercentertothe fieldandwefindthatthe cluster
as affects the properties of the galaxies up to two virial radii at z ∼ 0.35. Data suggest
: that during the last 3 Gyrs no evolution of the blue fraction, from the cluster core
v
to the field value, is seen beyond the one needed to account for the varying age with
i
X redshift of the Universe and of its content. The agreementof the radial profiles of the
blue fractionatz =0 andz ∼0.35implies that the patterninfalldidnotchangeover
r
a the last 3 Gyr, or, at least, its variation has no observational effect on the studied
quantity.
Key words: Galaxies: evolution — galaxies: clusters: general — galaxies: clusters:
1 INTRODUCTION ies,f ,isstillcontroversial.Thecontroversyisraisedbytwo
b
criticisms concerning measurements and sample.
The nature and the time scale of the processes that shape
galaxy properties in clusters and groups are still unclear. Andreon, Lobo & Iovino (2004; hereafter ALI04) anal-
The presence of a hot intercluster gas observed in X-rays yse three clusters at z ∼ 0.7 without finding evidence of a
should have a role in shaping some galaxy properties (e.g. high blue fraction with respect to z ∼ 0. They also show
Gunn & Gott 1972). The window opened by the redshift the drawbacks of the various definitions of f adopted in
b
dependence of the galaxy properties has been used to set the literature. They conclude then that “twenty years af-
constraintsonthetimescales oftheprocesses (e.g.Butcher ter the original intuition by Butcher & Oemler, we are still
& Oemler 1978, 1984; Dressler et al. 1997; Stanford, Eisen- in theprocess of ascertaining the reality of theeffect”. The
hardt & Dickinson, 1998; Treu et al. 2003). However, the sameworkputinadifferentperspectivetheresultsofRakos
observational evidence of the environmental effect is still & Shombert (1995), clarifying the fact that even if all the
uncertain. For example, the existence of a Butcher–Oemler galaxiesintheUniversearepassivelyevolving,thebluefrac-
(BO)effect(Butcher&Oemler1984),i.e.thefactthatclus- tion will be f ≈ 1 at z & 0.7 in the Rakos & Shombert
b
ters at higher redshift have a larger fraction of blue galax- (1995) scale. Therefore, the very high fraction they found
at high redshift does not require any special mechanism to
accountforthepresentdaycounterpartsotherthanageing.
⋆ [email protected] ALI04 introduce also a first discussion about the difficult
2 Andreon et al.
2 THE DATA & DATA REDUCTION
Table 1.Theclustersample
2.1 Photometry
Name z Nz σv error r200
km/s km/s Mpc We use the same imaging data as Andreon et al. (2004a),
with some additional observations taken in 2002 with the
XLSSC024 0.29 11 430 96 1.0 same instrument and telescope. Briefly, optical R– and z′–
XLSSC028 0.30 8 376 98 0.8
XLSSC009 0.33 12 236 52 0.5 band(λc ∼9000˚A)imageswereobtainedattheCerroTololo
Inter–American Observatory (CTIO) 4m Blanco telescope
XLSSC010 0.33 11 367 96 0.8
XLSSC016 0.33 5 915 294 2.0 duringthreeobservingruns,inAugust2000,November2001
XLSSC006 0.43 39 837 106 1.7 and September 2002 with the Mosaic II camera. Mosaic II
XLSSC012 0.43 12 741 165 1.5 is a 8k×8k camera with a 36×36 arcminute field of view.
Typicalexposuretimeswere1200 secondsin Rand2×750
seconds in z′. Seeing in the final images was between 1.0
and1.4arcsecondsFull–WidthatHalf–Maximum(FWHM)
intheSeptember2002 andNovember2001runs,and0.9to
task of measuring the error on fb, given the observations, 1.0 arcsec FWHM during the August 2000 run. The useful
showing that at least some previous works have underesti- nights of the three observing runs were photometric. Data
mated errors and, by consequence, overstated the evidence have been reduced in the standard way (see Andreon et al.
for the BO effect. The role of the inference, the logical step 2004a for details).
going from the observed data to the true value and its er- Source detection and characterization were performed
ror,hasbeenfurtherelaborated inD’Agostini(2004) inthe employingSExtractorv2(Bertin&Arnouts1996). Colours
more general case of unknown individual membership for and magnitudes are computed within a fixed 5 arcsecond
thegalaxies. radius aperture. A larger aperture, for colours, is used here
Kron (1994) claimed that all the “high” redshift clus- with respect to Andreon et al. (2004a), where 1.9 arcsec
ters known in the early 80’s (z ≈0.3−0.5) were somewhat was used, in order not to miss any potential star formation
extremeintheirproperties,andthiswaspreciselythereason occurring at radii not sampled by the previously adopted
why they were detected. Andreon & Ettori (1999) quantify aperture. Of course, results of that paper are unaffected by
this issue, and show that many of the clusters compared at ourpresent aperturechoice.
different redshifts have also different masses (or X-ray lu- Object magnitudes are quoted in the photometric sys-
minosities), in such a way that “we are comparing unripe temoftheassociated standardstars:Rmagnitudesarecal-
appleswithripeorangesinunderstandinghowfruitripens” ibrated with Landolt (1992) stars, while z′ magnitudes are
(Andreon & Ettori 1999). Together with Allison-Smith et calibrated with SDSS (Smith et al. 2002) standard stars.
al. (1993) and Andreon & Ettori (1999), ALI04 show that WekeepRandz′ magnitudesintheirsystem(i.e.Vegaand
the optical selection of clusters is prone to produce a bi- SDSS,respectively).
ased - hence inadequate - sample for studies on evolution
sinceat larger redshiftsit naturally favourstheinclusion in
thesampleof clusterswith asignificant bluefraction. They 2.2 Spectroscopy
showthatclusterswithabluefraction astheobservedones
Our clusters have been observed spectroscopically at Mag-
are over-represented in optical cluster catalogs by a factor
ellan, NTT or VLT (see Willis et al. 2005). Redshifts for a
two,withrespecttoidenticalclustersbutwithoutabursting
minimumof5upto39clustermembershavebeenacquired
population.
perclusterwithtypicalindividualerrorsonredshiftof50to
Thereisthereforeacompellingneedtostudytheprop-
erties of galaxies in clusters at intermediate redshift (z ≈ 150 km/s (depending on instrument, exposure time, etc.),
as detailed in thementioned papers.
0.35), avoiding the bias of an optical selection, by choosing
VelocitydispersionsarecomputedusingtheBeersetal.
clusters of the same mass as present day studied clusters
(1990) scale estimator, asdetailed in theAppendixand are
to avoid an “apple vs orange” issue. This is the aim of this
listed together with their errors in Table 1.
paper, where we present a BO–style study of a small but
representative sample of 7 clusters, X-ray selected, of low
to average mass (velocity dispersion) and at intermediate
redshift.
3 THE CLUSTER “APPLE VS ORANGE”
The layout of the paper is the following. In sect. 2 we
ISSUE
presentopticalimagingandspectraldata.Insect.3weshow
thatthestudiedsampleisbothrepresentativeandX–rayse- As discussed in the Introduction, the cluster selection cri-
lected.Werevisitinsection4thedefinitionofthebluefrac- teria should not bias the targeted measurement (the blue
tion,inordertoaccountforthereducedageoftheuniverse fraction). As mentioned, the optical selection, especially if
at higher redshift. Sect. 5 presents some technical details. performed in theblue band rest-frame, boosts by construc-
ResultsaresummarizedinSect.6,whereasSect.7discusses tion the blue fraction at high redshift, unless some precau-
relevant results published in the literature and some final tions are taken. The X–ray selection is useful because the
conclusions.AppendixespresentaBayesianestimateofclus- clusterX–rayemissivityisnotphysicallyrelated,inacause–
ter velocity dispersion, richness, and bluefraction. effectrelationship,tothecolourofclustergalaxies,theother
We adopt ΩΛ = 0.7, Ωm = 0.3 and H0 = 70 km s−1 factors (e.g. mass, dynamical status, etc.) being kept fixed.
Mpc−1. Fairleyetal.(2002)andWakeetal.(2005)exploitasimilar
BO effect at z ∼ 0.35 3
X–ray selection, for a cluster sample much more (the for- low),becauseitisquitedangeroustoattempttocorrectthe
mers) or slightly more (thelatters) massive (X–raybright), bluefraction for thebias induced by photometric errors. In
but statistically uncontrolled. fact,theunevencolourdistributionofgalaxies(forexample
The cluster sample studied in this paper is not an un- f = 0.2 means that more than 80 % of the galaxies have
b
controlled collection of clusters, but a random sampling of colours in a narrow red color range, and the remaining 20
an X–ray flux limited sample of clusters in a narrow red- % are spread over a large blue color range) and errors on
shift range (0.29 . z < 0.44), drawn from the ongoing colours of 0.2 mag amplitude produce a large Malmquist-
XMM-LSS survey (Pierre et al. 2004, and Pierre et al. in like(orEddington-like)bias, difficulttocorrect forwithout
preparation). The clusters actually used in the present pa- knowingthegalaxycolourdistribution,asfirstexplainedby
per are listed in Andreon et al. (2004a), or presented in a Jeffreys (1938). The Eddington (1940) reply to the Jeffreys
futurecatalogue.ThesamplestudiedhereisapurelyX–ray (1938)paperclarifiesthatimprovedvalues,i.e.correctedby
selectedonedrawnfromasampleconstructedusingbothan theerrormeasurements,“shouldnotbeusedforanykindof
X–rayandopticalselectioncriteria(theXMM-LSSsurvey), statistical inquiry” in good agreement with Jeffreys (1938).
asclarifiedbelow.WerefertoPierreetal.(2004)fordetails Iftheultimatelimit ofthemeasurementslaysinphotomet-
abouttheXMM-LSSsurvey,andwediscusshereonlysome ric errors, it is perhaps preferable to increase the quality of
relevant points. thephotometry, rather than increasing the size of the sam-
One great advantage of a volume complete sample (or ple,andthereforeweprefertohaveasmall,buthighquality
a random sampling of a volume complete sample) over an sample, than a large, low quality one.
uncontrolled one is that each object has a chance of occur- Malmquist-like biases affect our blue fraction determi-
ringthatisproportionaltoitsnumberdensity,i.e.occursin nation at z > 0.44, and therefore are of no concern for our
thesamplewiththesamenaturalfrequencyitoccursinthe analysis. However, they may be a concern for other sim-
Universe.Theabovepropertyisespeciallyusefulwhencom- ilar works. The above Malmquist-like bias, joined to the
putingensembleaverages (likecomposite clusters), because use of data with a fixed quality (such as those coming
itmakesthestatisticalanalysisstraightforward.Instead,av- from surveys) both unduly increase the observed fraction
erages performed over uncontrolled samples (e.g. combined of blue galaxies with redshift, simply because galaxies be-
“clusters”formedbystakingclustersfromuncontrolledlists) come fainter and photometric errors increase with redshift.
lackpredictivepowerbecausethesamplerepresentativityis TheaboveeffecthasnothingtodowiththeButcher-Oemler
unknown.Anastronomicalexample,togetherwithareal-life effect,ofcourse,becausetheamplitudeoftheeffectdepends
application of theabove concept is discussed in Sect 6.3.1. on the data quality,not on thegalaxy properties.
3.1 Malmquist-like (or Eddington-like) biases on 3.2 Which selection criteria?
f : redshift range selection
b Thesamplefromwhichwehavedrawnourclustersisformed
The precise choice of a redshift range largely depends on by all clusters detected both in X–rays and in the colour
the quality of the available optical photometry and on the space. Details about the colour detection can be found in
availability of velocity dispersions. The lower redshift limit Andreon et al. (2004a,b). At the redshift studied in this
(z∼0.29) hasbeenchosenbecauseofsaturationissues:our paper, clusters stand out in the colour–space, and also in
images are exposed too long for brighter objects and their the direct–space (i.e. in the sky plane) as shown in section
cores saturate, because exposure time has been originally 3.2 of Andreon et al. 2004a, i.e. the probability to miss in
optimized for thedetection of z ∼1 galaxies. The fuzziness the optical a cluster in the considered redshift range is vir-
of the nearest redshift limit is due to varying seeing condi- tually zero. In particular, clusters at z 6 0.29 stand out
tions and sky brightness during theobserving runs. in the direct–space (i.e. on images) so conspicuously that
Theupperredshift limit (z =0.44) comesfrom ourde- their brightest galaxies saturate the instrument (exposure
sire to get a complete and unbiased sample. At z > 0.44 time is tuned for z ∼ 1 galaxies). Can a cluster get unno-
not all clusters have a known velocity dispersion, and it is ticed when its galaxies (almost) saturate the instrument?
legitimatetosuspectthatclusterswithoutaknownσv have Therefore, even if in principle our cluster sample is drawn
a different blue fraction from clusters with a known σv, all from a sample that uses two criteria (X–ray emission and
the remaining parameters being kept fixed. Indeed, a clus- colour-detection), at the studied redshifts the colour selec-
terwithalargernumberofredgalaxieshas,observationally, tion does not bias the cluster selection because it does not
betterchanceof havingalarger numberofconfirmedmem- filter out any object. To check the above, during the spec-
bers than an equally rich, but poor in red galaxies, cluster, troscopiccampaign wedevoteda(small) fraction oftimeto
because background galaxies are more aboundant among spectroscopicallyconfirmcandidatesnotmeetingthecolour
blue galaxies in percentage. Clusters rich in blue galaxies detection.Noneturnsouttobeconfirmedintheconsidered
may haveso few confirmed members that a cluster velocity redshift range, showing that if clusters of galaxies not de-
dispersion cannot be computed with a sufficient accuracy. tectable in the colour-space do exist, they are so rare that
Therefore, a cluster with a small blue fraction has a bet- they are not likely to occur in a sample like ours. As an in-
ter chance to have a measured velocity dispersion than one dependentcheck, we spectroscopically confirmed colour de-
with a large blue fraction. Below z =0.44, all clusters have tected clusters without detectable X-ray emission, at the
aknownvelocitydispersionandthisproblemdoesnotarise. same and higher redshift, showing that the optical selec-
In general, an upper redshift limit is needed for an- tiongoesdeeperintheclustermassfunctionthantheX-ray
other reason: we want the faintest considered galaxies to selection. One such an example, RzCS 001 at z = 0.49 is
be still affected by a negligible photometric error (see be- listed in Andreon et al. (2004a). Anotherone, RzCS 052 at
4 Andreon et al.
z=1.02isstudiedinAndreonetal.(2005).Thepresenceof early–typegalaxiesattheclusterredshift(theclusterredse-
other clusters deliberately not studied in this paper in the quence).Thegalaxieshavetobecounteddowntoagivenab-
very same studied volume of Universe, such as RzCS 001, solutemagnitudewhichischosentobeMV =−19.3magin
emphasizes once morethat we are studingan x-ray selected ourcosmology (−20 mag in BO cosmology), within a refer-
cluster sample and clarifies that the adopted selection is a enceradiusthatencompassesagivenfractionofthecluster.
deliberated choice in order to avoid the bias of the optical Moreover,galaxieslocated inthebackgroundorforeground
selection at high redshift, not an obliged choice dictated by of the cluster must be removed, for example by statistical
our ignorance about which otherclusters are present in the subtraction.
studied volume of theUniverse. TheactuallimitingmagnitudeusedintheBOpaperis,
attheBOhighredshiftend,brighterthanMV =−19.3mag
inourcosmology (−20magintheBOcosmology) asshown
3.3 Random sampling from a complete sample by de Propris et al. (2003), i.e. different from what the BO
definition requires.A brighterlimiting magnitude at higher
Inside the selected redshift range, we removed all clusters
redshift is thecorrect choice if one wants to track thesame
with r200 radii overlapping each other in the sky plane or populationofgalaxiesatdifferentredshifts,becauseofaver-
which exceed the studied field of view of each individual
age luminosity evolution experienced by galaxies. Galaxies
CTIOpointing(∼0.3deg2 area,tokeepuniformqualityall havingat z =1 MV =−19.3 mag are now (at z=0) much
acrossthearea),aswellasoneXLSSCclusterthatlacksan fainter than the MV = −19.3 mag cut. A fixed magnitude
obvious center. These (observational–driven) cluster selec-
cutthereforedoesnotselectsimilargalaxiesatdifferentred-
tionsareindependentontheclusterbluefractionandhence
shifts, whereas an evolving limit does. Therefore, we have
producenobiases. Therefore, oursample constitutes a ran-
adopted an evolving mag limit, as actually adopted by BO
domsamplingofXMM-LSSclustersintheselected redshift
themselves. An evolving limiting magnitude has also been
range.
adopted by de Propris et al. (2003), Ellingson et al. (2001)
and ALI04 in their BO–style studies.
ALI04 discuss the large impact that apparently minor
3.4 Details about the X-ray selection
differencesonthef definitionhaveontheobservedf .They
b b
Asmentioned,oursampleisdrawnfromtheXMM-LSS,and found that:
thereforeoursampleinheritsitsadvantagesandlimitations. – the reference colour of the early–type galaxies to be
To a first approximation, the survey is flux limited, and usedistheobservedcolouroftheredsequence,andnotthe
therefore brighter clusters, visible over larger volumes are colour of a present day elliptical, unless we are happy with
in principle over-represented in the survey. However, here an evolving fb fraction for a sample of galaxies passively
the studied redshift interval is small (∆z = 0.14), and the evolving;
effect should be minor. –thereferenceradiusshouldscalewiththeclustersize,
Furthermore, the XMM-LSS is surface brightness lim- and not be a fixed metric radius, potentially sampling the
ited too, as most existing surveys, in spite of the use of center of rich and large clusters and the whole cluster for
waveletsinthedetectionsteptomitigatesurfacebrightness small groups (another“apples vsoranges” issue);
effects. Extensive numerical simulations (Pacaud et al., in –aunique∆shouldbetaken(equalto0.2intheB−V
preparation) showthat, for core radii typicalof thestudied rest–frame). If different values are chosen at different red-
objects,detectabilityislargerthan90%forallourobjects. shifts, it becomes difficult to compare populations selected
X-ray fluxes inside half the optical r200 radius (com- with heterogeneous choices.
putedasspecifiedinSec5)werecomputedinthe0.5−2keV Let usdiscuss, and revise, the∆ choice.
band from MOS1, MOS2 and pn merged images processed There is little doubt that galaxies at higher redshift
as in Chiappetti et al. (2005). We assumed a Raymond - have younger stars than present day galaxies, as measured
Smith spectrum with kT = 2 keV and z = 0.35, and the by thefact that thereddest galaxies havea colour that be-
average galactic column density in the XMM-LSS (Dickey comes bluer in the rest–frame with increasing redshift (e.g.
&Lockman,1990).Wefoundfouroursystemsvaluesinthe Stanford et al. 1998, Kodama et al. 1998, Andreon et al.
range 0.3 . Lx . 16 1043 erg s−1 cm−2 in the 0.5−2 keV 2004a). This isalso thenaturaloutcome of thecurrent cos-
band. mological modelthatallocates ashorterage oftheuniverse
at higher redshifts. At the time of the BO paper, the mea-
To summarize, the studied sample has 0.3 . Lx .
surementofthebluefractionwasavaluableevidencetorule
16 1043, and it has been selected in a redshift-luminosity-
outanon-evolvinguniverse.However,iftheaimofderiving
surface brightness region where detectability is near 100 %,
the f fraction is to measure an evolution beyond the one
b
sothateachclusterhasthesameprobabilityofoccurringin
due to the younger age of the universe at high redshift, we
our sample as in theUniverse.
propose a different choice for ∆, using an evolving spectral
template in order to coherently separate blue galaxies from
red ones. This is also an observationally obliged choice, as
shown below.
4 THE GALAXY “APPLES VS ORANGES”
Figure1clearlyillustratesforourchoice.Theleftpanel
ISSUE
shows the rest–frame B−V colour of τ = 1 (upper curve)
Butcher & Oemler (1985) define the fraction of blue galax- and τ =3.7 (lower curve) Bruzual & Charlot (2003) stellar
iesin thecluster, f ,asbeingthefraction of galaxies bluer, populations of solar metallicity for exponentially declining
b
by at least ∆ = 0.2 mag in the B −V rest–frame, than starformation ratemodels,whereτ isthee–foldingtimein
BO effect at z ∼ 0.35 5
Figure 1. Left panel: rest–frame B−V colour of a τ = 1 Gyr and zf = 11 stellar population (top red line, mimicking an E), and a
stellarpopulation havingthesamezf butbeing0.2magbluertoday, i.e.τ =3.7Gyr,zf =11,referredinthispaperastoSa(bottom
blue line). Right panel: R−z′ colour difference in the observer rest frame between the two above stellar populations (solid line). The
dottedlinerepresentsthedifferenceforthecaseofnonagingstellarpopulations.DottedcirclesarederivedusingtheColeman,Wuand
Weedman(non–evolving) templates.Thetwovertical(green)delimitersmarktheredshiftrangeprobedinthispaper.
Gyr. The formation redshift, z = 11, and e–folding time, values are found, even for a fixed galaxy sample, because a
f
τ = 1, are both chosen to reproduce the observed R−z′ non-evolvingandanevolvingtemplateonlymatchatz=0.
colour of our clusters over 0.3 . z < 1 (those of this pa- In fact, Fairley et al. (2002) found that the blue fraction
per, and those presented in Andreon et al. 2004a), and the is higher if a bluer rest–frame set of filters is used. Thus,
typicalcolourof present–dayellipticals, B−V ∼0.95 mag. some galaxies turn out to be either blue or red depending
This population is referred as to the spectro–photometric ontheselectedfilterset,althoughthetwoclassesshouldbe
elliptical one. The e–folding time of the bluer track is cho- separated.
sen to have a present day colour B −V = 0.75 mag, i.e.
The upper solid curve in the right panel of Fig. 1 re-
0.2 mag bluer than an elliptical, as the BO definition re-
inforces the conclusion of the above discussion, but in the
quires (i.e. ∆ = 0.2 mag). We refer this template as to
observerrest–frame.Thecontinuouslinemarkstheexpected
thespectro-photometricSa,forsakeofclarity.Inagreement R−z′ colourdifference,intheobserverbands,foranevolv-
with Butcher–Oemler, at z ∼ 0 this spectral template is ing template having ∆(B−V)=0.2 today, i.e. considering
the appropriate one to discriminate between red and blue
our evolving Sa spectral template. The dashed curve illus-
galaxies.However,thetwotracksdonotrunparallel,which trates the R−z′ colour difference that one would incor-
meansthatwhatischaracterizedtodayby∆=0.2magwas
rectlyuseifnostellarevolutionwasallowedfor.Ithasbeen
∆ > 0.2 mag in the past (at higher redshift). This reflects
computed for a non–evolving Sa template. Finally, the cir-
thefactthatatthattimetheuniverse,anditscontent,were cles show the R−z′ colour difference one should derive by
younger.Thechoiceofafixed∆allowsgalaxies, eventhose
using non–evolving templates taken from Coleman, Wu &
with simple exponential declining star formation rates, to
Weedman (1980), as usually done. There is a rather good
move from the blue to the red class, as time goes on (as
agreement between the latter track and our non–evolving
redshift becomes smaller). That drift boosts the blue frac-
Sa track over a large redshift range (0.3 < z < 0.7): it re-
tionf at highredshift.Sincethechoiceofafixed∆allows
b flects the fact that the spectra of the two templates agree
a possible drift from one class to the other, and assuming
with each other at z=0 overa large wavelength range and
that a redshift dependence is found for the blue fraction,
that our Sa model reasonably describes (at the requested
does the above tell us something about the relative evolu-
resolution) the observed spectra of Sa galaxies in the local
tion of red and blue galaxies? It merely reflects a selection
Universelisted in Coleman, Wu & Weedman (1980).
biasrelatedtothewaygalaxiesaredividedincolourclasses:
To conclude, we definitively adopt an evolving Sa tem-
a class naturally gets contaminated by the other one. This
plate to differentiate between blue and red galaxies, i.e. an
is precisely what Weiner et al. (2005) observed.
evolving ∆ colour cut as shown by the solid curve in the
Fromanobservationalpointofview,measurementsare right panel of Fig. 1. Galaxies bluer than a Sa spectral–
rarelytakeninfiltersthatperfectlymatchB andV.There- templatearereferred toas“blue”,thoseredder,“red”.The
fore, the colour cut is computed using a spectral template. bluefractionisthereforecomputedwithrespecttoagalaxy
Thelatterisusuallytakenfrom theColeman, Wu&Weed- model that quietly forms stars as ourSamodel. Ourchoice
man (1980) spectrum, i.e. for a non-evolving template. If has the advantage of focusing on galaxy evolution, instead
the blue fraction is computed in such a way, then different of focusing on observational problems related to the filter
6 Andreon et al.
Figure 2. Colour–magnitude diagram for galaxies within r200. Only galaxies brighter than the evolved MV = −19.3 mag (indicated
with a spline curve) are shown. Colours are corrected for the colour–magnitude relation. The solid (dashed) line marks the expected
colourofanevolvingE(Sa)spectraltemplate.
choice or of assuming an unphysical universe, in which the r200 = σ1D (1)
age of the Universe does depend on redshift, but in which H0p30[Ωm(1+z)3+ΩΛ]
theage of its content does not.
(Mauduit,Mamon,&Hill,2005)whereσ1D istheclus-
tervelocity dispersion. Found valuesare listed in Table 1.
– the center of the cluster is defined by the position of
the brightest cluster member (BCM), with one exception:
XLSSC 006 has two BCMs, and we took the cluster center
5 TECHNICAL DETAILS
at the middle of the two. The adopted center is compatible
Beforeproceedingwiththecalculationofthefractionofblue with the detected X–ray center. Their precise location is
galaxies fb, several additional operations need to be made: unimportant for measurements performed within r200
– the colour red sequence is derived from the median – Galaxies redder than an Sa are referred to as red
colourofthethreebrightestgalaxiesconsideredtobeviable galaxies(sect 4),buthowfarinthereddirection shouldwe
clustermembers,i.e.galaxiesthataretooblueortoobright integrate the colour distribution? We adopted several cuts
to beplausibly at thecluster redshift are discarded. (including +∞), and in six out of seven cases, we find no
– the slope of the observed colour–magnitude relation evidence for a bias in the measured f for any cut redder
b
is removed from the data. The slope is an eyeball fit to the than the colour of an E +0.05 mag, i.e. we find no sta-
observedcolour–magnitudeofgalaxiesintheclustercenter, tistical evidence for a cluster population redder than the
in order to limit the background contribution. We measure colour–magnitude sequence plus 0.05 mag. Actually such a
0.025 colour mag per unit mag at the studied redshifts. population is not expected from population synthesis mod-
–theadoptedradiusthatencloseanoverdensityof200 els, because the reddest model galaxies have the colour of
times thecritical density:r200, computed from therelation theredsequencegalaxies.Bykeepingthesmallestvalue(the
BO effect at z ∼ 0.35 7
Figure 3. Colour distribution of galaxies located within r200 and brighter than the evolved absolute magnitude MV = −19.3 along
theline-of-sightofthecluster(solidhistogram)andinthecontrol field(dashedhistogram),normalizedtotheclusterarea.Coloursare
corrected for the colour–magnitude relation. The right(left) arrow marks the expected colour of an evolving E (Sa) template. Colours
arebinned,andconsequently resolutionisdegraded, fordisplaypurposesonly.
colourofanE+0.05 mag) wemaximizetheS/Noftheblue 6 RESULTS
fraction determination, without biasing themeasurement.
6.1 Colour–magnitude and colour distribution
–Whenselectingthebackgroundregion,wechoosethe The colour–magnitude relation and colour distribution of
most representative realization of the control field: all the three (out of seven) clusters in our sample are presented in
regions which are not associated with the target, i.e. such Andreon et al. (2004a), and discussed there with 15 addi-
thatr>2r200.Thepreciseradiusused(sayr/r200 >2or5) tionalclusters.Hereweonlywanttodiscusswhatisdirectly
isirrelevant,becausethecontributionofgalaxiesintheclus- relevant for theBO effect.
teroutskirtsisnegligiblewithrespecttothenumberoffield Figure2showstheobservedcolour–magnituderelation
galaxiesinourhugecontrolarea(approximatively0.3deg2). forgalaxieswithinr200(includingbackgroundgalaxies),cor-
Other researchers prefer instead to choose the background rected for the colour–magnitude slope (sec 5), and differ-
area in regions particularly devoided of galaxies, hence un- ence in seeing between the R and z′ exposures (sec 2.1).
duly boosting the number of members and apparently re- The solid line marks the expected colour of the assumed
ducingthe noise in thef estimate. spectro-photometric E template discussed in sect. 4. There
b
isagoodmatchbetweentheexpectedandobservedcolours
of the red sequence for six out of seven cases. The red se-
– We verified that our galaxy catalogs are complete quence of XLSSC 016 is slightly bluer (by 0.05 mag) than
down to MV = −19.3 mag (and fainter magnitudes), as in expected, a feature that can be better appreciated in Fig.
previousworks(e.g.Andreonetal.2004; Garilli, Maccagni, 3.This single(out of seven),and admittedlysmall, offset is
Andreon 1999). not in disagreement with our error estimate for the colour
8 Andreon et al.
Table 2.Bluefractionsofindividualclustersforgalaxieswithin
r200
Name Ngal error fb 68%c.i.
XLSSC024 24 8 0.09 [0.02,0.17]
XLSSC028 14 7 0.06 [0.01,0.11]
XLSSC009 9 5 0.09 [0.01,0.17]
XLSSC010 24 8 0.51 [0.33,0.68]
XLSSC016 51 15 0.45 [0.29,0.61]
XLSSC006 204 21 0.43 [0.38,0.48]
XLSSC012 8 7 0.16 [0.02,0.31]
Ngal is the number of galaxies inside r200 and brighter
thantheevolvedMV =−19.3mag.
calibrationofabout.0.03mag(Andreonetal.2004a),and
thereforesuchaminormismatchhasbeencorrectedfor(by
shifting the R−z′ colour by this amount), in the f de-
b
termination, but has been left untouched in Figs. 2 and 3
to allow the reader to appreciate it. Unduly neglecting the
abovecorrectioninducesabias(actuallyasystematicerror)
of 0.01 in f . The error bar on f (including everything in
b b
theerror budget) turnsout to be16 times larger.
Figure 3 shows the colour histograms of galaxies
brighter than the evolved MV = −19.3 mag located along
the line-of-sight of the cluster (solid histogram) and in the
control field (dashed histogram, ∼0.3 deg2), normalized to
theclusterarea.Thecontrolfieldistakenfromthesameim-
agewheretheclusterisobserved,andhencesharesthesame
photometriczero–point andquality.Therefore, anysystem-
aticphotometric errorlargely simplifies in thebluefraction
determination,becausebothcolourdistributionsareshifted
by thesame amount (includingthe case of XLSSC016).
6.2 Blue fractions for individual clusters
Table 2 summarizes our point estimate of the cluster rich-
ness,thebluefractionfb,anditsassociatederror,computed Figure 6. Relationship between cluster velocity dispersion and
as described in Appendix B and C. Shortly, we introduce bluefractionwithin r200 (top panel)andwithin r200/4(bottom
methodsofwidespreaduseinthestatisticalcommunity,but panel).Inthetoppanel,thelinearmodelfavouredbythedatais
largely unused in previous BO studies, which are more ro- shown.
bust than traditional methods. Instead of introducing an
estimator for the blue fraction and of providing a point es-
timateofitwhich,inthelongrun(i.e.ifwewereallowedto assumption for the prior (an upside-down parabola in the
repeat the observations a large number of times), tends to [0,1] range and 0 outside), in order to quantify the robust-
thequantityaimed tomeasure (thebluefraction), wecom- ness of the results on the assumed prior. The latter prior
putetheprobabilityofeachvalueofthebluefraction,given quantifiestheexpectationofsomereaders,whobelievethat
the data, using the Bayes theorem of statistics. Bayesian aButcher–Oemlereffectexists,i.e.whobelievethatlowval-
inferenceisfreefromlogicalcontradictionsofassigningneg- ues of the blue fraction are unlikely a priori. The parabolic
ative (or complex) values to positively defined quantities, prior encodes such a belief, un–favouring low values of the
that affected many previous BO studies. bluefraction. Comparison between Figs 4and 5showsthat
Richness (N in Table 2) is computed for galaxies ourpointestimatefortheclusterbluefraction(themedian,
gal
brighter than the evolved −19.3 mag and are located in- that by definition falls in the center of the highlighted re-
side r200. Ourclusters are quite poor, on average, although gion) anditserror (thewidthof thehighlighted region) are
they show a large range of richnesses. onlymarginallyaffectedbythechoiceoftheprior,ifaffectes
Figure4showsthe(posterior)probabilitythatourclus- it at all.
tershaveafraction fb ofbluegalaxieswithinr200 assuming Threeclustershaveabluefractionwithinr200 ofabout
a uniform prior. The 68 % central credible intervals (er- 0.4, whereas the other four clusters display a blue fraction
rors)aredrawnasshades.Theyareusuallysmall(∼±0.1), of the order, or less than, 0.1. More precisely, the richest
in spite of the fact that many of our clusters contain few clusters seem to possess the largest blue fractions. What is
members. Figure 5is similar to Fig 4, butundera different the statistical significance of such a relationship, shown in
BO effect at z ∼ 0.35 9
Figure 4. Probabilityfor fb at r200 assuming auniform prior.The shaded regions delimitthe 68 % interval (error). At its center lies
ourpointestimateoftheclusterbluefraction.Eachpanelismarkedbythelastthreedigitsoftheclustername.
Figure 5.AsFig5,butforaparabolicprior.
Fig6?Liddle(2004) remindedtheastronomical community However, theadopted model appears to beunphysical,
of the difficult problem of model selection, i.e. in our case, because for clusters having σv < 200 km s−1, it predicts
toestablishwhetherexistingdatasupportamodelinwhich f < 0. A more complex model is required, that perhaps
b
the blue fraction fb depends on σv. Our compared mod- flattensoffatlow σv,avoidingunphysicalfb values.Atthis
els (a constant f vs a linear relationship between f and moment, we consider such a model too complex, given the
b b
σv) are nested and regularity conditions hold in our case. available set of data. Evidence for a possible correlation is
The likelihood ratio turns out to be 2∆logL ∼ 6.6 when recognized but it is considered far from being definitive.
adding one more parameter. Therefore, under the null hy- Evidenceforacorrelationbetweenthebluefractionand
pothesis(aconstantfb)thereisa1%probabilitytoobserve the velocity dispersion largely disappears when choosing a
alargerlikelihoodratiobyaddingonemoreparameter.Fur- smaller reference radius (say r200/2 or r200/4), as shown in
thermore, theBayesian Information Criterium (BIC) intro- the bottom panel of Fig. 6 for r200/4. Of course, a shallow
ducedbySwartz(1978),anddescribedinvariousstatistical relationshipcouldbepresent,butourdatadonotunambigu-
textbooks (and also in Liddle 2004) offers another way to ouslyfavourit,becausetherelationship, ifany,isswamped
look at the same problem, in the Bayesian framework. A by the relative importance of errors. The possible lack of
value of 6 or more is regarded as strong evidence against a relationship between the central blue fraction and mass
the model with a larger value of BIC whereas a value of (measured by the cluster velocity dispersion) seems to con-
twoisregardedaspositiveevidence(Jeffreys1961).Wefind firm a similar lack of correlation between the cluster X-ray
∆BIC = 5.8 in favour of the model fb ∝ k(σv −200). To luminosity (a tracer of mass) and the central blue fraction
summarize, there seems to be some good evidence for the (Andreon& Ettori 1999; Fairley et al. 2002).
existence of a linear relationship between fb and σv. At low redshift (z <0.1), Goto et al. (2003) and Goto
10 Andreon et al.
Table3.Radialdependenceofthebluefractionofthecombined
sample
Sample Ngal error fb error
r<r200 321 32 0.33 0.04
r<r200/4 136 13 0.24 0.04
r200/4<r<r200/2 109 16 0.30 0.07
r200/2<r<r200 78 25 0.46 0.10
r200<r<1.5r200 48 25 0.55 0.14
field 83 10 0.73 0.05
sample to be a representative one, otherwise the computed
averagewouldlackitspredictivepower.Oursampleissmall,
but constitutes a representativesample of clusters (sect 3).
6.3.2 Radial dependence of the blue fraction in the
composite sample
Differentphysicalmechanismsarethoughttooperateindif-
Figure 7.Constraintsonfb forthecombinedsample. ferent environments (see Treu et al. 2003 for a summary)
and thus, by identifying where the colour of galaxies starts
(2005) tentativelyconcludefrom alarger sample of clusters to change, we can hope to identify the relative importance
thatthereisnoevidenceforarelationshipbetweentheblue of such mechanisms. For this reason, we studied the radial
fraction and the cluster mass. However, their definition of dependenceofthebluefractionfb asusuallydoneinthelit-
theblue fraction is different from ours, and theirstatistical erature, by splitting the data in radial bins. We arbitrarily
analysisisverydifferent(forexampleGotoet al.2003 have choose[0,1/4],[1/4,1/2],[1/2,1]and[1,1.5]inunitsofr200,
observedseveralclusterswithunphysicalvaluesfortheblue for simplicity. In the outermost bin we were forced to drop
fraction,seetheirFig1).Similarly,Baloghetal.(2004)find XLSSC016,because1.5r200 liesfartherawaythanthemid-
noevidence at z <0.08 for a relationship between thefrac- distance between XLSSC 016 and the nearest cluster to it,
tion of blue galaxies inside the virial radius and the veloc- asseenprojectedontheplaneofthesky,and,therefore,this
ity dispersion, although, admittedly, fairly large uncertain- radialbinispotentiallycontaminatedbygalaxiesbelonging
ties affect their results, besides another definition of what totheothercluster.Notethatitsinclusion,orexclusion,in
is “blue”. Whether the relationship sets itself at redshifts theotherradial binsdoesnotaffect thederivedvalues,and
higherthanthoseprobedbyGoto etal.orBalogh etal., or therefore our conclusions. Table 3 lists thefound values.
whetheritismaskedatlowredshiftbecauseoftheirvarious Figure 8 (solid points) shows that the blue fraction in-
blue fraction definitions or because of the way the analysis creases with theclustercentric distance, from 0.24±0.04 in
is performed, or, finally, is the result of a small sample at theinnermostbin,to0.46±0.10and0.55±0.14in thetwo
z∼0.35, is still a matter tobe investigated. outermostbins:galaxiesatthecenterofclustersarefoundto
haveasuppressedstarformation(reddercolours)compared
to those at larger clustercentric radii.
6.3 Composite sample Havewereachedthefieldvalueofthebluefraction?Us-
ingthespectrophotometrylistedinCOMBO-17(Wolfetal.
6.3.1 Blue fraction of the composite sample
2004),thatencompasses1/4deg2oftheChandraDeepField
Figure7showsthe(posterior)probabilitythatthecombined region,wehaveselectedthegalaxiesbrighterthanthe(same
samplehasabluefractionf ,computedusingrecursivelythe evolving)absolutemagnitudelimitadoptedinourwork,and
b
Bayestheorem.Itisbell–shapedandnarrow,thatmakesthe in the same redshift range (0.29 < z < 0.44). There are 83
blue fraction in the composite sample well determined and galaxies,ofwhich61arebluerthananSaevolvingtemplate.
independentonprior:f =0.33±0.05.Thecombinedsample We,therefore,inferabluefractionof0.73±0.05,arbitrarily
b
is formed by about 320 cluster galaxies within r200. plotted at r/r200 = 2.5 in Fig. 8. In the above calculation,
What does this result mean in the presence of a pos- we were forced, for lack of information, to neglect redshift
sible relationship between the velocity dispersion and the errors and errors on thephotometric corrections applied by
bluefraction?Theexistenceofmeasurementsclaimedtobe theauthors to computeabsolute magnitudes.
incompatibledoesnotconstituteanabsoluteobstacle when Thebluefraction isfoundtosteadily increasefrom the
computingasampleaverageintheBayesianframework,pro- cluster core to thefield value.
vided that the studied sample constitutes a representative The important point to note in Fig 8 is that the influ-
one.Itisinoureverydayexperiencetocomputemeansofa enceoftheclusterreacheslargeradii.Therearetwopossible
populationinwhichtheelementsdiffermuchmorebetween explanations for the above result. First, the mechanism af-
each other than the uncertainties affecting the individual fectingthegalaxycoloursreacheslargeradii.Insuchacase,
measurements (cf. the average post-doc salary, the average ram pressure stripping, tidal halo stripping and tidal trig-
human weight or height, etc.). These averages require the geringstarformation(justtomentionafew,seee.g.Treuet